Formula For Coriolis Force

Coriolis Force Formula:

\[ F_c = -2 m (\omega \times v) \]

Mass (m):

Angular Velocity (ω):

rad/s

Velocity (v):

m/s

Angle between ω and v:

degrees

Coriolis Force (F_c):

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1. What is the Coriolis Force Formula?

The Coriolis force formula describes the fictitious force that appears in rotating reference frames. It acts perpendicular to the velocity of a moving object and the axis of rotation, affecting the trajectory of objects in rotating systems.

2. How Does the Calculator Work?

The calculator uses the Coriolis force formula:

\[ F_c = -2 m (\omega \times v) \]

Where:

\( F_c \) — Coriolis force (N)
\( m \) — Mass of the object (kg)
\( \omega \) — Angular velocity vector (rad/s)
\( v \) — Velocity vector of the object (m/s)
\( \times \) — Cross product operation

Explanation: The formula calculates the magnitude of the Coriolis force, which is proportional to the mass, angular velocity, velocity, and the sine of the angle between the angular velocity and velocity vectors.

3. Importance of Coriolis Force Calculation

Details: The Coriolis force is crucial in meteorology for understanding weather patterns, in oceanography for ocean currents, in ballistics for projectile motion, and in various engineering applications involving rotating systems.

4. Using the Calculator

Tips: Enter mass in kilograms, angular velocity in radians per second, velocity in meters per second, and the angle between the angular velocity and velocity vectors in degrees. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the Coriolis force called a "fictitious force"?
A: It's called fictitious because it appears only in rotating (non-inertial) reference frames and doesn't result from physical interactions between objects.

Q2: How does the Coriolis force affect weather patterns?
A: On Earth, it deflects moving air masses to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, creating cyclonic weather patterns.

Q3: What is the significance of the negative sign in the formula?
A: The negative sign indicates that the Coriolis force acts in the direction opposite to what would be expected from a simple cross product, ensuring proper directional relationships.

Q4: When is the Coriolis force maximum?
A: The Coriolis force is maximum when the velocity vector is perpendicular to the angular velocity vector (90° angle), and zero when they are parallel (0° or 180°).

Q5: Does the Coriolis force do work on objects?
A: No, the Coriolis force always acts perpendicular to the velocity vector, so it does no work and doesn't change the kinetic energy of the object.